Theory in and for mathematics education: in pursuit of a critical agenda

This special issue of Educational Studies in Mathematics, developed from the Mathematics Education and Contemporary Theory (MECT) conferences in Manchester, U.K., follows up an earlier double special issue in Volume 80 (2012) of this journal, which comprised 18 papers authored from a dozen countries. These efforts—both in conference and in print—to develop theory in and for mathematics education should be seen as part of our community’s collective effort to offer mathematics education broader yet more rigorous “thinking tools”. We argue in this introduction that in these times where ideology so often defines “improvement” in preference to rigorous analysis, this effort is more important than ever before. The selected papers span two broad areas: theory is used to develop critical conceptual frameworks for studies in mathematics education by Llewellyn, Nolan, Barwell, Nardi, Pais; and philosophical dimensions of mathematical learning are discussed by Ernest, Skovsmose, and Boylan.

School mathematics is increasingly viewed as part of the armoury deployed in responding to political demands for economic and technological development. Schooling in general, and mathematics education in particular, is increasingly shaped, funded and judged by its perceived capacity to deliver success in terms of the prescribed quantitative measures by which so many governments reference their ambitions and achievements. Good performance here has sometimes been taken as being indicative of wider economic potential: the policy rhetoric suggests that the more we can improve in those areas the better for our future national well being. Governments of right and left have been seduced by the appeal of “raising standards” in a statistically defined world, in which standards become a fetish for intellectual life and academic achievement (Strathern, 2000). Measures of school performance developed in various international exercises now often define what education is for or what it should be, policing educational boundaries with ever-greater efficiency. These instruments have transformed the content of what they purported to compare, and similarly threaten to transform the demands on teachers and pupils preparing to meet these newly defined challenges. A key effect is a convergence of the metrics that produce normalcy, equating compliance with particular patterns of achievement with being “good” or “better”. Policy thus legislates for a particular version of mathematics according to a centralised script, normalising what it is or should be to be a mathematics teacher (Nolan, this volume) and what it is or should be to be a mathematics student (Llewellyn, this volume). Thus, political exigency finesses educational ethics. Such is the banality of the new bureaucratic control exercised by these new technologies.

This political control is exercised in the name of economic efficiency, responding to the new market in educational performativity and has consequently reframed how funded research in mathematics education is conceived, prescribed, evaluated, and so conducted. Market metaphors abound in the language of improvement, with terms like progress, advance, quality, effectiveness, industry, competitiveness, performance, and standards slipping easily off the tongue in much of the contemporary academic discourse. A better TIMSS or PISA result becomes spoken of as an indicator of better teaching, and policy-makers and researchers seek models to follow from those countries that are doing well in their league table. Hence, much research is often predicated on improving school achievement in standardized terms rather than merely studying it and understanding it. Proposals for funding typically must offer victory narratives, making promises of how research outcomes will provide specific understandings of education and so improve it. References to such discourses seem often to shape the activity of aspirational individual researchers. The superlatives used in the construction of these narratives, however, can sometimes disguise the differences between the multiply directed motivations of mathematics education researchers (e.g., for ethical practices, to understand more deeply, to disrupt or think differently) and the operational motives that guide their actions (e.g., securing funding, getting published, recalibrating practice, working towards a PhD, etc.). The requirement that research should reach agreement with politicians and employers across nations might be a further stretch.

But theory suggests that “improvement” and similar aspirational metaphors for the passage of time can be understood in many ways. Academic motives and ethics for working with children in school such as enjoyment of mathematics, mathematical integrity, and functionality in practical situations do not always pull in the same direction as “improvement” or its metrics (Boylan, this issue). A choice has to be made as to the sort of mathematical activity that is worth living, and what or who it is for or against. Do we want to invest funds in centres of excellence in learning at the expense of wider inclusion? Should mathematics be promoted at the risk of discriminating against certain students or promoting dominant political agenda? Should mathematical understanding be conflated with functional technology? We might even ask whether functional mathematics and its pedagogy is inhibited by overly-asserted notions of certainty (Ernest, this issue). Further, the advance of mathematics is not always desirable. Often the economic drivers of research in mathematics are not decided by altruistic purpose or ethical priorities. Our access to scientific and mathematical phenomena is mediated by “multiple foregrounds” (Skovsmose, this issue) and is affected by the way in which we apprehend their purpose and accept the challenge of engaging with them as “imaginations, possibilities, obstructions, hopes, fears, stereotypes, and preconceptions”.

Contemporary politics then is complicated by the disjunction of governmental politics—despite being cravenly discoursed in market metaphors—and the real operation of the market (Pais, this issue), which forces the hand of states to adopt certain forms of policy. Thus, market conditions can often trump educational principles in setting the terms of educational practices. That is, it can be unclear how a researcher in mathematics education might seek to conceptualise the challenge of researching the field with a view to asserting some instrumental impact. Impacting on policy is not only unlikely, as politicians do not always listen to or connect with mathematics education researchers, but even if they were to be more attentive the impact of any given policy is highly uncertain. However, this macro perspective evades many researchers in mathematics education who focus on their own local situations, without any specified ambition of scaling up for a wider population.

A major challenge then is to rethink the breadth of mathematics education in resistance to reductive conceptions of mathematics, and to critique mathematics education conceived of and (re-)created in support of current models of economic production, technology, and political administration. This is a key task for theory and theory development and alone justifies its importance to the mathematics education community.